Measurement of the $\tau$ Lepton Mass and an Upper Limit on the Mass Difference between ${\tau }^{+}$ and ${\tau }^{-}$

The mass of the $\tau$ lepton has been measured in the decay mode $\tau \to 3\pi {\nu }_{\tau }$ using a pseudomass technique. The result obtained from $414{\mathrm{fb}}^{-1}$ of data collected with the Belle detector is $M_{\tau }=[1776.61\pm 0.13(\mathrm{stat})\pm 0.35(\mathrm{sys})]\mathrm{MeV}/c^2$. The upper limit on the relative mass difference between positive and negative $\tau$ leptons is $|M_{{\tau }^{+}}-M_{{\tau }^{-}}|/M_{\tau }<2.8\times {10}^{-4}$ at 90% confidence level.

Figure 1

The pseudomass distribution $M_{\min }$ for the ${\tau }^{\pm }\to 3{\pi }^{\pm }{\nu }_{\tau }$ candidates. The points with error bars are data and the solid line is the result of the fit with the function (2).

Figure 2

The $[M({\mu }^{+}{\mu }^{-})-2E_{\mathrm{beam}}]$ distributions for the data (points with errors) and Monte Carlo calculations (histogram without errors). The curves show the results of the fit to the data and Monte Carlo calculations by the sum of two Gaussians multiplied by a cubic polynomial.

Figure 3

The distribution of the pseudomass $M_{\min }$ for the decay $\tau \to 3{\pi }^{\pm }{\nu }_{\tau }$, shown separately for positively and negatively charged $\tau$ decays. The solid points with error bars correspond to ${\tau }^{+}$ decays, while the open points with error bars are ${\tau }^{-}$ decays. The solid curve is the result of the fit to the pseudomass distribution of ${\tau }^{+}$ with function (2) while the dashed one is for the ${\tau }^{-}$.